Properties

Label 1386.2.w
Level $1386$
Weight $2$
Character orbit 1386.w
Rep. character $\chi_{1386}(353,\cdot)$
Character field $\Q(\zeta_{6})$
Dimension $160$
Sturm bound $576$

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Defining parameters

Level: \( N \) \(=\) \( 1386 = 2 \cdot 3^{2} \cdot 7 \cdot 11 \)
Weight: \( k \) \(=\) \( 2 \)
Character orbit: \([\chi]\) \(=\) 1386.w (of order \(6\) and degree \(2\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 63 \)
Character field: \(\Q(\zeta_{6})\)
Sturm bound: \(576\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{2}(1386, [\chi])\).

Total New Old
Modular forms 592 160 432
Cusp forms 560 160 400
Eisenstein series 32 0 32

Trace form

\( 160q - 160q^{4} - 4q^{7} - 8q^{9} + O(q^{10}) \) \( 160q - 160q^{4} - 4q^{7} - 8q^{9} - 12q^{13} + 12q^{14} + 28q^{15} + 160q^{16} + 36q^{17} + 8q^{18} + 4q^{21} - 24q^{23} - 80q^{25} - 36q^{27} + 4q^{28} - 12q^{29} + 8q^{36} + 4q^{37} + 4q^{39} + 12q^{41} + 4q^{43} + 12q^{45} - 12q^{46} + 72q^{47} + 16q^{49} - 24q^{50} - 8q^{51} + 12q^{52} + 48q^{53} - 36q^{54} - 12q^{56} - 16q^{57} - 28q^{60} - 72q^{62} - 92q^{63} - 160q^{64} + 56q^{67} - 36q^{68} + 84q^{69} + 24q^{70} - 8q^{72} - 36q^{74} + 36q^{75} + 8q^{79} + 40q^{81} - 4q^{84} - 24q^{86} + 36q^{87} - 12q^{89} - 36q^{90} + 24q^{91} + 24q^{92} + 56q^{93} - 12q^{97} + O(q^{100}) \)

Decomposition of \(S_{2}^{\mathrm{new}}(1386, [\chi])\) into newform subspaces

The newforms in this space have not yet been added to the LMFDB.

Decomposition of \(S_{2}^{\mathrm{old}}(1386, [\chi])\) into lower level spaces

\( S_{2}^{\mathrm{old}}(1386, [\chi]) \cong \) \(S_{2}^{\mathrm{new}}(63, [\chi])\)\(^{\oplus 4}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(126, [\chi])\)\(^{\oplus 2}\)\(\oplus\)\(S_{2}^{\mathrm{new}}(693, [\chi])\)\(^{\oplus 2}\)